Erdős problem 15

Is it true that $\sum_{n=1}^\infty(-1)^n\frac{n}{p_n}$ converges, where $p_n$ is the sequence of primes?

Sources

The source's own material, retained exactly.

1 retained statement36c6d0fef71a

Open selected source

FormalConjectures/ErdosProblems/

15.lean

Retained formal statement1 of 1

Is it true that $\sum_{n=1}^\infty(-1)^n\frac{n}{p_n}$ converges, where $p_n$ is the sequence of primes?

Note: In the problem statement, $p_n$ is the $n$ -th prime, indexed such that $p_1=2, p_2=3, \ldots$ . We 0-index here to reflect how Nat.nth works.

FormalConjectures/ErdosProblems/15.leanErdos15.erdos_151 lineExact file

1True ↔ Summable fun k => (-1) ^ (k + 1) * (↑k + 1) / ↑(Nat.nth Nat.Prime k)

OpenStatement only, no proof